Section profiles for planing hydrofoils and hydrofoils operating close to a free water surface

ABSTRACT

A hydrofoil section comprising upper and lower cambered profiles and a reference line in which: the reference line is drawn between the trailing edge of the section and the leading edge or a point close to and below such leading edge, and both profiles have a positive camber, and a substantial part of the lower profile lies above such reference line, and the area bounded by such reference line and by such lower profile lying above such reference line is greater than any area lying below such reference line.

This invention relates to a new form of sections for hydrofoils forhigh-speed marine craft. The sections are configured such that theyprovide both high lift coefficients and high ratios of lift to drag overa wide range of craft speeds, whether running submerged in closeproximity to the free surface of the water or planing thereon. In thiscontext the expression “running submerged in close proximity to the freesurface of the water” means a hydrofoil which is designed to operate ata depth/chord ratio preferably of less than one.

The invention has particular application to the use of high speedcatamarans and other surface craft which can benefit from the greatlyreduced power consumption and improved ride and handling provided.

Whilst the majority of applications are likely to be for faster craft,the lift and drag characteristics of the new sections are such thatsignificant reductions in hull resistance have been recorded atdisplacement Froude numbers only a little above 1.0 such that the newsections also have application to relatively heavy commercial andworkboats.

Once fully planing the lift to drag ratio increases steadily with speedsuch that the power requirement remains relatively constant over a widespeed range, essentially only increasing due to the increasing windresistance.

The displacement Froude number Fn_(V) is given by the followingexpression:

Fn _(V) =V/√(g·Δ ^(1/3))

where V is the velocity of the craft, Δ is the volume of water displacedby the hull when it is at rest and g is the rate of acceleration due togravity (all in consistent units)

This invention has for objectives:

To provide hydrofoils having reduced variation in lift coefficient withimmersed depth variation;

To provide hydrofoil sections with much improved lift/drag ratios underdeeply submerged, shallowly submerged and planing conditions;

To provide sections ideally suited to the new concept of planinghydrofoils and the corresponding benefits of sharply reducing resistancewith increasing speed;

To provide rapid and certain means for designing and optimisinghydrofoil sections, particularly those intended for shallow immersionand planing conditions

Preferred examples of hydrofoil sections will now be described withreference to the accompanying drawings.

FIG. 1 shows the variation of the lift coefficient of typicalsub-cavitating hydrofoil sections designed for operation at a depthbelow the water level operating at a constant angle of attack at varyingdepth of submergence;

FIG. 2 shows the variation of the lift coefficient of cavitatinghydrofoil section operating at a constant angle of attack at varyingdepth of submergence;

FIG. 3 shows the variation of the ratio of the lift coefficient atvarious depth/chord ratios relative to the lift coefficients at infinitedepth of typical hydrofoil sections;

FIG. 4 shows the variation the chord Frauds Number F_(c) with craftspeed for a hydrofoil section of unit chord;

FIG. 5 shows the variation of the lift/drag ratios with the liftcoefficient based on the span of planing hydrofoils of aspect ratiosvarying between 2.5 and 12 operating at a constant angle of attack andwith varying camber;

FIG. 6 shows the variation of the lift/drag ratios with the liftcoefficient of planing hydrofoils of aspect ratios of 5 and 10 havingconstant section operating at varying angles of attack;

FIG. 7 shows a hydrofoil section according to the present invention withconstruction lines for its creation;

FIG. 8 shows a detail of the leading edge geometry of the hydrofoilsection of FIG. 7;

FIG. 9 shows an alternative hydrofoil section according to the presentinvention with construction lines for its creation;

FIG. 10 shows a modification of the hydrofoil section of FIG. 9;

FIG. 11 shows an evolution of the pressure distribution during theoptimisation process of the design of a hydrofoil according to thepresent invention;

FIG. 12 shows a hydrofoil section according to the present invention;

FIG. 13 shows an alternative hydrofoil section according to the presentinvention;

FIG. 14 shows the hydrofoil section of FIG. 12 operating at a depthbelow the free water surface;

FIG. 15 shows the hydrofoil section of FIG. 12 operating at a depthbelow the free water surface in which a cavitation bubble has formedclose to the leading edge;

FIG. 16 shows the hydrofoil section of FIG. 12 operating at a depthbelow the free water surface in which the upper surface of the sectionis fully ventilated;

FIG. 17 shows the hydrofoil section of FIG. 12 in which a trailing edgeflap is deflected downwards operating at a depth below the free watersurface in which the upper surface of the section is fully ventilated;

FIG. 18 shows the hydrofoil section of FIG. 12 which is fully planing;

FIG. 19 shows the hydrofoil section of FIG. 12 operating at its designspeed with a reduced effective chord between a forward spray rootposition and the trailing edge;

FIG. 20 shows the hydrofoil section of FIG. 12 which is fully planingwith the flap deflected downwards;

FIG. 21 shows the hydrofoil section of FIG. 13 which is fully planing;

FIG. 22 shows the hydrofoil section of FIG. 13 which is fully planingwith the trailing edge flap deflected downwards;

FIG. 23 shows the hydrofoil section of FIG. 13 which is fully immersed;

FIG. 24 shows the hydrofoil section of FIG. 13 which is fully immersedwith the trailing edge flap deflected downwards;

FIG. 25 shows the pressure distribution around the hydrofoil section ofFIG. 12 which is fully immersed;

FIG. 2S shows the pressure distribution around the hydrofoil section ofFIG. 12 which is fully planing at its design condition;

FIG. 27 shows the pressure distribution around the hydrofoil section ofFIG. 13 which is fully immersed and the distribution around a NACA 67A709 section for comparison;

FIG. 28 shows the desired pressure distribution around the hydrofoilsection of U.S. Pat. No. 3,946,680;

FIG. 29 shows the computed pressure distribution around the hydrofoilsection of U.S. Pat. No. 3,946,688 under particular operatingconditions;

FIG. 30 shows the computed pressure distribution around the Speera H105hydrofoil section operating deeply immersed;

FIG. 31 shows section profiles for the sections of FIGS. 12 and 13together with a NACA 67A 709 and a Speer H105 section in which thethickness is shown exaggerated;

FIG. 32 shows deeply immersed characteristics of the profiles of FIGS.12 and 13 together with a NACA 67A 709 and a Speer H105 section;

Referring to FIG. 1 curves 1 show a rapid reduction in lift coefficientfor sub-cavitating sections as the hydrofoil nears the water surface.Although not shown on this figure the lift/drag ration also falls awaydue to the an increasing effect of the friction drag. Initially thisreduction is quite slow, but as the value of d/c approaches 0.25 thereduction in the lift/drag ratio becomes increasingly marked. Curve 11shows the variance of the lift coefficient with the depth/chord ratiofor an efficient hydrodynamic section with a slightly concave undersurface. Curve 12 shows the variance for a more classic aerofoil sectionwhich a slightly convex under surface. The difference is due to theincreasing reliance on the pressure distribution on the lower surface asa cavitation bubble increasingly grows on the upper surface whichbecomes fully ventilated at some point. Both sections have a 2D liftcoefficient of 0.63 when deeply immersed.

Referring to FIG. 2 the opposite effect is evident for cavitatingsections. For the flat plate shown by curve 2 the lift coefficientdoubles between deep immersion and zero immersion with most of thisoccurring when the hydrofoil is very close to the surface. The curve formore efficient cavitating sections follows the same trend although theoverall increase in lift coefficient is reduced from 100% to generally25% to 50%. The lift/drag ratio for a cavitating section tends toimprove as the surface is approached. The frictionless value tends to belittle changed but the friction coefficient has a reducing effect as thelift coefficient increases close to the surface,

Referring to FIGS. 3 and 4 it is evident that the lift coefficient isincreasingly reduced as the depth/chord ratio reduces, particularly inthe region around a chord Fronde number of 1, where the chord Froudenumber is given by the expression

F _(c) V/√(g·C)

where V is the velocity of the craft, C is the chord of the hydrofoilsection and g is the rate of acceleration due to gravity (all inconsistent units).

Line 4 of FIG. 4 shows the variation of F_(c) with craft speed for achord of one metre from which it can be seen that a significantreduction in lift coefficient is to be expected as the hydrofoil sectionapproached the surface, particularly in the range of speeds from 5 to 10m/sec at which a high lift coefficient may be required to get a craftfoil borne.

It will be evident from FIGS. 1, 2, 2 and 4 that the design of asuitable section is highly dependent on the range of immersion depthintended, particularly if operation within the range of immersion depthsbetween 0.5 and zero is expected.

Referring to FIGS. 5 and 6 the benefit is shown of using the a planinghydrofoil section arranged for constant wetted span in which the chordreduces and by consequence the aspect ratio increases as the speedincreases. FIG. 5 shows the rapid improvement in the lift/drag ratio asthe aspect ratio is improved. It also shows that the camber andassociated value of the lift coefficient based on span must be carefullyselected to lie within a desired range of lift/drag values. FIG. 6 showsvalues of CL and the lift/drag ratio for hydrofoils having aspect ratiosor 5 and 10 with the same section with the lift coefficient varied bychanging the angle of attack. These curves show the importance ofmaintaining an optimum angle of attack with the performance droppingaway rapidly as the angle of attack is increased. The aspect ratio isequally of key importance.

Referring to FIG. 7 and FIG. 8 a hydrofoil section 401 is shown togetherwith details 300 for designing such profile. An upper section 4014 maybe created by drawing a conic between points 302, 305 and 306 in which aweight may be assigned to curve point 305. A straight line may be drawnbetween points 306 and the trailing edge point 307. An aft lower section4017 may be created by drawing a further conic between points 307, 308and 309 and a weight assigned to the curve point 308. A mid lowersection 4018 may be created by drawing a further conic between points309, 310 and 311 and a weight assigned to the curve point 310. A linemay be drawn between points 311 and 303 to create the forward undersidesection 4015. Referring to FIG. 8 a leading edge section 4012 may becreated by drawing a conic between points 303, 301 and 302 which passesthrough the leading edge point 304. Alternatively the leading edgesection 4012 may be created by drawing two conics between points 303,3031 and 304 and between 304, 3021 and 302 and weights assigned to curvepoints 3021, 3031. In order to fine tune the pressure distributionaround the leading edge it is sometimes beneficial to move the leadingedge point 304 upwards or downwards along the line between points 3021and 3031 and to consider assigning different weights to curve points3021 and 3031 in order to provide a local inflexion in the mean camberline in the leading edge section 4012. Straight lines and conicalsections are preferentially arranged to be tangent continuous other thanat the curve or apex points of the conical sections and at the trailingedge.

Referring to FIGS. 9 and 10, a mixture of conics and lines may be usedto create sections 402 and 403 using the above techniques

Referring to FIG. 11, the selection of curve points and weights andfeeding the resulting profiles into a computational fluid dynamics (CFD)analysis software package the pressure distribution and other sectionalattributes may be produces for deeply immersed, shallowly immersed orplaning conditions. FIG. 11 shows pressure distribution curves 100acting on the upper surface and 110 acting on the lower surface ofhydrofoil sections produced using FIG. 9 with curves 101, 102, 103 and104 produced by assigning different curve point weights to points 3021,3031 and 30 and by omitting or including point 306. By combining a pointcreation code and a CFD code sections conforming to particular designcriteria may be produced and optimised automatically providing muchfaster and much smoother sectional profiles than have been heretoforepossible. This is particularly the case for shallowly immersed sectionsand for planing sections for which neither software nor standardprofiles are available. Whilst planing profiles have not heretoforeexisted, shallowly immersed sections for use with hydrofoil assistedcatamarans and other hydrofoil craft have generally been poorlyspecified,

Referring to FIGS. 12 and 13 profiles 401 of FIGS. 7 and 402 of Figurehave been extracted. FIG. 12 shows a new profile for planing or shallowimmersion characterised by a pronounced ‘bustle’ 4017 at the aft end ofthe lower surface an inflexion curve 4018 ahead of the ‘bustle’, a flator slightly convex forward section 4015 and a relatively sharp leadingedge 4012. For some applications a more curved leading edge similar tocurve 4022 of FIG. 13 may be applied. FIG. 13 is more similar toclassical aerofoils but with key differences which are described below.This profile is generally better suited to slower craft and relativelydeeper immersion. Flaps 4011, 4021 (not illustrated) may be applied tothe sections shown.

Referring to FIGS. 14 to 17 section 401 of FIG. 12 is shown at generallyincreasing speed and decreasing immersion. In FIG. 14 the section isfully immersed and fully wetted. The leading edge is shown at a depth dbelow the free surface 201. The water surface 202 immediately ahead ofthe hydrofoil 401 and for some distance (not shown) aft of the hydrofoilis distorted by the thickness or the hydrofoil and by the lift itgenerates. In the submerged state the camber line 502 shows asignificant camber 503 from the chord reference line 500. Although themean camber line 502 is shown following aeronautic practice it isgenerally more useful for hydrodynamic purposes to consider the camberof the upper and lower lifting surfaces separately. FIG. 15 shows acavitation bubble 205 starting to form at the leading edge. FIG. 15shows the upper surface of hydrofoil 401 fully ventilated with an upperventilation boundary 203 and a low ventilation boundary 204. Figureshows a reduced immersion depth d, with a trailing edge flap 4011deflected downward increasing the camber 503. This would correspondgenerally to a. ‘lift-off’ condition for a craft.

Referring to FIGS. 18 to 20 which show hydrofoil profile 401 operatingin a fully planing state. In Figure the profile is just fully planingwith the free surface water level 201 at or close to the leading edge.The camber 501 is now defined by the lower surface of profile 401 andreference line 500 drawn between the trailing edge 4013 and a pointtangential to the lower curved leading edge section 4012 or to theintersection between the lower surface of the leading edge section 4012and the forward underside section 4015 of FIG. 12. The camber is muchreduced relative to the camber 503 of the immersed section of FIG. 14indicating a large reduction in lift coefficient compared to the fullyimmersed section. However, as above noted for hydrofoil sections it ismore useful to consider the cambers of the upper and lower sectionsseparately rather than the shape of the mean camber line 502 usuallyconsidered in aeronautic practice. If so considered there is lesssignificance between the camber of the lower immersed surface and theplaning surface of the section 401. The camber to effective chord ratiois given by the length of line 501 divided by the length of theeffective chord line 500 and is 2.15% in this condition for this section401. The maximum camber point is well aft being situated 82.4% from thefront of the effective chord line. By reference the maximum camber ofthe lower surface of a NACA 67A 709 section measured in the same manneris 0.64% at 80.2% chord. FIG. 19 shows the profile at or close to itsdesign condition in which the forward end of the chord is now defined bythe spray root generated by the planing section. The camber 501 issomewhat increased in this condition such that the camber/chord ratio issubstantially increased to 4.5 positioned 65.5% along the effectivechord line indicating a significant increase in lift coefficient. Inthis condition the angle of attack is substantially reduced such thatthe lift/drag ratio is substantially increased. FIG. 20 shows thehydrofoil profile 401 with a trailing edge flap deflected downwardsresulting in a further increase in camber 501 to 3.6% of the effectivechord positioned 84.4% along the effective chord line. This conditioncorresponds to the status immediately post becoming foil-borne for apreferred case where a flap is fitted,

FIGS. 21 and 22 refer to section 402 of FIG. 13 without and with thepresence of a downwardly deflected flap 4021 and in the fully planingstate. For the unflapped case the camber 501 is very small for thissection with a camber/effective chord ratio of 1.11% at 83.5% of chord.Due to the relatively larger leading edge thickness of section 402compared to section 401 it can be expected that the spray root pointwill form at a point 515 some distance aft of the leading edge. With adownward flap deflection of 10 degrees these figure become respectively3.8% and 80.7%.

FIGS. 23 and 24 correspond to the hydrofoil profile of FIG. 13 in thefully immersed and fully wetted condition and show the high camber 513for this section in this condition.

Referring to FIG. 25 which shows the pressure distribution for thehydrofoil profile 401 of FIG. 12, the upper line 101 shows a relativelyhigh negative pressure extending across virtually the whole chord. AHigh negative pressure spike just aft of the leading edge will result inthe early formation of a cavitation bubble in the area and assists thetransition to fully ventilated flow. The key feature of this profile isthe high positive pressure acting on the underside of the profileparticularly ahead of the trailing edge and the complete absence ofareas of negative pressure at all expected angles of attack as shown bycurve 1115, out 33% of the total lift is due to the positive pressureacting on the underside of the hydrofoil section. At slow speed the highlift coefficient has the effect of lifting the craft. As the speedbuilds the upper part of the section start to ventilate, but thepositive pressure acting on the underside increases in line with curve 2of FIG. 2

Referring to FIG. 26, line 111W shows the positive pressure distributionacting on the underside of section 410 in the design planing state.Under this condition the effective chord is designed to reduce to about55% of the total chord as the section lifts partially out of the water.The figure of 55% will vary from section to section and depends on theratio of foil-borne speed to maximum design speed for the craft inquestion. Comparing curve with the aft 55% of curve 1115 of FIG. 25 itcan be seen that the pressure distributions are virtually the sameexcept that in the planing state the pressure coefficient tends to zerorather than unity. The section characteristics show q relatively highlift coefficient and an extremely high lift/drag ratio compared to otherplaning or cavitating sections. This is due to the fact that a higher‘bustle’ can be used for this innovative planing section than would bepossible for a cavitating submerged section in that the upper cavity isventilated and consequently higher than for a submerged section and thatthe extended chord increases the height under the cavity boundary. Also,once planing there is no flow over the hydrofoil section other than,perhaps, under wave conditions so any notion of cavity thickness fallaway.

Referring to FIG. 27, pressure distribution curves are shown for thehydrofoil profile 402 of FIG. 13 and for a NACA 67A 709 section underdeep immersion conditions. It can be seen that curve 102 showing thecomputed negative pressure for profile 402 is more constant and extendsover a greater area than for the NACA profile consequently increasingthe lift with little or no effect on cavitation or ventilationinception. The greater differences are however between curves 112 and113 showing the pressure distribution on the underside of the sections.Here it will be seen that the positive pressure is higher for curve 113right across the chord, but particularly so towards the trailing edge.This has a major impact on the lift/drag ratio. Additionally, the NAsection has a negative pressure zone on the underside which will resultin cavitation on this surface at higher speeds which will have a verynegative impact on performance at higher speeds. The new section 402shows no negative pressure zone on the underside all normal angles ofattack.

With reference to FIGS. 28 and 29 shown for the much studied sectionsaccording to U.S. Pat. No. 3,946,688, whilst FIG. 28 shows a moderatelyadvantageous pressure distribution, the distribution calculated for thecase of FIG. 29 is very poor with large areas of negative pressure onthe underside both in the region of the leading edge and the flap pivot.The lift would fall away very quickly for this section as it approachedthe free surface.

With reference to FIG. 30, the pressure distribution is shown for a muchused Speer H¹⁰⁵ hydrofoil section. This section was designedspecifically for use with hydrofoils but is very unsuited to shallowimmersion operation. Lines 104 and 114 show the pressure distributionfor the upper surface and the lower surface of the profile respectively.The large negative pressure extending over much of the lower surfacewill result in a sharp fall in lift as the section approaches the watersurface. Even for normal operation the fact that both the upper and thelower surface produce negative lift with only a small pressuredifferential means that the lift/drag ratio is poor. The peak negativepressure on the upper surface is not high, but it is high relative tothe lift coefficient.

With reference to FIG. 31, section data for the new profiles 401/4011,402/4021 is shown together with NACA 67A 709 profile 403/4031 and SpeerH105 sections 404/4041.

With reference to FIG. 32 it is shown that the new sections no onlyexhibit much improved pressure distribution, but also higher liftcoefficients and very much higher lift/drag ratios. The overallthickness for the sections is similar other than for the thicker Speersection. Critically, the positive lift generated by the underside of thesection is significantly higher for the new sections.

Whilst the figures show two particular preferred embodiments of thecurrent invention it will be clear that the methodology of the presentinvention may be used to design optimised hydrofoil profiles for anycondition of depth, speed and required lift coefficient.

1. A hydrofoil section comprising upper and lower cambered profiles anda reference line in which: the reference line is drawn between thetrailing edge of the section and the leading edge or a point close toand below such leading edge, and both profiles have a positive camber,and a substantial part of the lower profile lies above such referenceline, and the area bounded by such reference line and by such lowerprofile lying above such reference line is greater than any area lyingbelow such reference line.
 2. The hydrofoil section according to claim 1comprising a point of maximum camber of the lower profile measured fromthe reference line which is situated at a point not exceeding 50% of thelength of the reference line measured from the trailing edge of thesection.
 3. A hydrofoil section according to claim 1 in which the lowerprofile has a camber exceeding 1% of the length of its reference line.4. A hydrofoil section according to claim 1 in which a significant partof the lower profile extending from a point close to the leading edge ofthe section is made up of a generally straight or slightly curved linewhich is generally parallel to the reference line.
 5. A hydrofoilsection according to claim 4 in which the generally straight portionextends over a length exceeding 10% of the length of the reference line.6. A hydrofoil section according to claim 1 which comprises at least oneconic such that the section pressure and velocity characteristics may bevaried by adjusting the position of such conic or conics and byadjusting the weight assigned to any vertex or curve point thereof.
 7. Ahydrofoil section according to claim 6 entirely created from conics andstraight lines.
 8. A hydrofoil section according to claim 7 in whichlines are arranged to be tangent continuous other than at any vertex orcurve point of any conic section and at the trailing edge.
 9. Ahydrofoil section according to claim 7 in which the section shape andhydrodynamic characteristics are optimised by alteration of the pointsand conic vertex or curve point weights within a computer programme.